Soil Reinforcement System Including Angled Soil Reinforcement Elements To Resist Seismic Shear Forces And Methods Of Making Same

ABSTRACT

A soil reinforcement system including angled soil reinforcement elements to resist seismic shear forces and methods of making same are disclosed. For example, the soil reinforcement system includes an array or grid of angled soil reinforcement elements installed within the ground, wherein the angled reinforcement elements are designed to absorb and/or resist earthquake-induced seismic shear forces by transferring the applied shear forces into axial compressive and tensile forces within each of the angled reinforcement elements.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to and incorporates by reference U.S.patent application Ser. No. 13/912,986 filed Jun. 7, 2013, entitled“Soil Reinforcement System Including Angled Soil Reinforcement ElementsTo Resist Seismic Shear Forces And Methods Of Making Same” that claimspriority to U.S. Provisional Application Ser. No. 61/656,687 filed Jun.7, 2012, entitled “Method and Apparatus for Creating Inclined SoilReinforcement Elements to Resist Seismic Shear Forces,” the disclosuresof which are expressly incorporated by reference herein in theirentirety.

TECHNICAL FIELD

The presently disclosed subject matter relates generally to mechanismsfor resisting earthquake seismic shear stresses and forces and moreparticularly to a soil reinforcement system including angled soilreinforcement elements to resist seismic shear forces and methods ofmaking same.

BACKGROUND

Earthquakes occur as a result of tectonic activity. When earthquakesoccur they shake the bedrock in the vicinity of the fault rupture thatresults in shearing stresses applied to the soil column above the rock.Pore fluid is the groundwater held within a soil or rock; namely, in thegaps between particles (i.e., in the pores). Pore water pressure refersto the pressure of groundwater held within the pores of the soil orrock.

Seismically-induced shearing forces propagate upwards through the soilprofile, often resulting in damage to existing structures and sometimesresulting in soil liquefaction. Liquefaction is a phenomenon that occursin saturated soils that involves the transfer of the effectiveoverburden load from the soil grains to the pore fluid, with thecommensurate reduction in effective stress and, hence, reduction in soilstrength. In earthquake-induced liquefaction, this transfer is initiatedin sandy soils by the collapse of the soil skeleton due to earthquakeshaking. Following liquefaction, settlement occurs as the pore waterpressures dissipate. Soil liquefaction can result in billions of dollarsin structural damage and can lead to a loss of life.

Many methods are available to mitigate the effects of soil liquefactionor to render the soil non-liquefiable. Deep foundations (e.g., drivenpilings, drilled concrete-filled shafts) can be used to bypass theliquefiable soil and reduce the effects of liquefaction. Dynamiccompaction, vibroflotation, and the installation of stone columns aresome methods used to densify clean granular soils and thereby reduceliquefaction potential. Vertical stiff inclusions have also been used toabsorb seismic shear stresses to reduce liquefaction potential. However,this method is partially limited in its effectiveness because theelements, if sufficiently slender, inherently are more efficient atresisting shear forces through flexure (i.e., bending) in lieu of shear.

SUMMARY

In one aspect, the presently disclosed subject matter relates to amethod of installing one or more angled soil reinforcement elements toresist seismic shear stresses. The method comprises inserting an angledstiff element into a soil matrix at a determined angle and to adetermined depth. The one or more angled stiff elements preferably havea sufficient rigidity and area ratio such that seismic shear stressesimparted from seismic activity are transferred to the angled stiffelement, thus reducing a potential for soil liquefaction. The one ormore angled stiff elements may be inserted in the soil matrix bydrilling means or by driving means. The one or more angled stiffelements comprise a material that exhibits a stiffness modulus greaterthan that of the soil matrix, which may comprise metallic material,non-metallic material, or a combination of metallic and non-metallicmaterials. In one embodiment, the one or more angled stiff elements areinstalled in an array.

The determined depth of the one or more angled stiff elements may beselected based on the in-situ liquefaction susceptibility of the matrixsoil. The spacing and diameter of the one or more angled stiff elementsmay be determined such that the transfer of the seismic shear stressesto the elements is sufficient to reduce the shear strains in the soil toreduce the triggering of liquefaction. The angle of inclination may be apredetermined angle based on desired installation and load transferefficiency criteria.

The one or more angled stiff elements may comprise cast-in-place shaftsthat are formed in the soil matrix. The shafts may be filled withconcrete and/or grout. The one or more angled stiff elements may beinstalled using a mandrel driven or pushed into the ground and filledwith the concrete and/or grout, and then the mandrel is extracted. Themethod may further comprise forming an angled drilled hole in the soilmatrix and filling the angled hole with the concrete and/or grout.Reinforcing steel may also be added to the concrete and/or grout shaftsprior to curing.

The one or more angled stiff elements may be installed in the soilmatrix by piling equipment and may be driven or pushed into the soilmatrix and may be filled with an in-fill after driving. The one or moreangled stiff elements may be hollow and may be filled with an in-fillmaterial after installation. In-fill material may comprise one or moreof concrete, grout, gravel, aggregate, sand, recycled concrete, crushedglass, or other flowable or pumpable material. Further, the in-fillmaterial may be compacted in place using a compaction device. In oneembodiment, the one or more angled stiff elements may comprise amaterial with high permeabilities that facilitate drainage of excesspore water pressures during and after seismic events.

The one or more angled stiff elements may be installed on a gridpattern. The method may also further comprise a second grid pattern ofone or more angled stiff elements angled 180 degrees from the first gridpattern of the one or more angled stiff elements. The method may alsocomprise a second grid pattern of one or more angled stiff elementsinstalled in the transverse direction to that of the first grid patternof the one or more angled stiff elements. The transverse direction ofthe second grid pattern may be either perpendicular to the first gridpattern or not perpendicular to the first grid pattern.

In another aspect, the presently disclosed subject matter relates to anangled stiff element for resisting seismic shear stresses. The angledstiff element has a sufficient rigidity and area ratio such that seismicshear stresses are transferred to the angled stiff element, thusreducing a potential for soil liquefaction. The angled stiff element maycomprise a material that exhibits a stiffness modulus greater than thatof a matrix soil in which it is installed.

In a further aspect, the presently disclosed subject matter relates to asystem for installing one or more angled soil reinforcement elements toresist seismic shear stresses and forces. The system comprises: a) oneor more angled soil reinforcement elements and b) a device forinstalling the one or more angled soil reinforcement elements into asoil matrix at a determined angle and to a determined depth. The devicefor installing the one or more angled soil reinforcement elements intothe soil matrix may comprise a piling device for driving or pushing theone or more angled soil reinforcement elements into the soil matrix. Thedevice for installing the one or more angled soil reinforcement elementsinto the soil matrix may also comprise a mandrel driven or pushed intothe soil matrix, the mandrel is filled with grout and/or concrete, andthen the mandrel is extracted. The device for installing the one or moreangled soil reinforcement elements into the soil matrix may alsocomprise a drilling device. In one embodiment, the drilling device formsan angled drilled hole in the soil matrix and the hole is then filledwith concrete and/or grout.

BRIEF DESCRIPTION OF THE DRAWINGS

Having thus described the presently disclosed subject matter in generalterms, reference will now be made to the accompanying Drawings, whichare not necessarily drawn to scale, and wherein:

FIG. 1 and FIG. 2 illustrate a side view and top down view,respectively, of an example of a soil reinforcement system that includesangled reinforcement elements for absorbing earthquake-induced seismicshear stresses and forces in accordance with the present invention;

FIG. 3 illustrates a side view of one angled reinforcement element andshowing more details thereof;

FIG. 4, FIG. 5, and FIG. 6 illustrate side views of a process of formingand installing an angled reinforcement element according to oneembodiment of the invention,

FIG. 7 illustrates a flow diagram of an example of a method of formingand installing the angled reinforcement element of FIG. 4, FIG. 5, andFIG. 6;

FIG. 8 and FIG. 9 illustrate side views of a process of forming andinstalling an angled reinforcement element according to anotherembodiment of the invention;

FIG. 10 illustrates a flow diagram of an example of a method of formingand installing the angled reinforcement element of FIG. 8 and FIG. 9;

FIG. 11 and FIG. 12 illustrate side views of a process of forming andinstalling an angled reinforcement element according to yet anotherembodiment of the invention;

FIG. 13 illustrates a flow diagram of an example of a method of formingand installing the angled reinforcement element of FIG. 11 and FIG. 12;

FIG. 14 shows a schematic of the transfer of seismic shear forces to theangled reinforcement element and to the matrix soil around the angledreinforcement element in accordance with the present invention;

FIG. 15 shows a schematic of the load transfer mechanism provided by thepresent invention loaded by one shear force;

FIG. 16 shows a schematic of the propagation of the distribution ofsinusoidal shear stresses applied within unreinforced soil mass at twotime intervals for a simulated earthquake;

FIG. 17 shows a schematic of the load transfer mechanisms provided bythe present invention loaded by two shear forces;

FIG. 18 shows a plot of the normalized shear stress vs. normalized depthfor an array of angled reinforcement elements of the present invention;and

FIG. 19 shows a plot of the normalized shear stress vs. normalized depthfor an array of conventional prior art vertical elements.

DETAILED DESCRIPTION

The presently disclosed subject matter will now be described more fullyhereinafter with reference to the accompanying Drawings, in which some,but not all embodiments of the presently disclosed subject matter areshown. Like numbers refer to like elements throughout. The presentlydisclosed subject matter may be embodied in many different forms andshould not be construed as limited to the embodiments set forth herein;rather, these embodiments are provided so that this disclosure willsatisfy applicable legal requirements. Indeed, many modifications andother embodiments of the presently disclosed subject matter set forthherein will come to mind to one skilled in the art to which thepresently disclosed subject matter pertains having the benefit of theteachings presented in the foregoing descriptions and the associatedDrawings. Therefore, it is to be understood that the presently disclosedsubject matter is not to be limited to the specific embodimentsdisclosed and that modifications and other embodiments are intended tobe included within the scope of the appended claims.

In some embodiments, the presently disclosed subject matter provides asoil reinforcement system including angled soil reinforcement elementsto resist seismic shear forces and methods of making same. Inparticular, the invention is directed to a soil reinforcement system forand methods of installing angled reinforcement elements within theground, wherein the angled reinforcement elements are designed to absorband/or resist earthquake-induced seismic shear forces by transferringthe applied shear forces into axial compressive and tensile forceswithin each of the angled reinforcement elements.

In one aspect, a soil reinforcement system and method is provided forthe installation of angled reinforcement elements in soils subject toearthquake ground motions. A method consists of inserting an angledreinforcement element with a sufficient rigidity and area ratio into thesoil profile such that the seismic shear stresses are transferred to theangled reinforcement element, thus reducing the potential for soilliquefaction. The angled reinforcement elements may be inserted bydrilling, driving, or other means and may consist of metallic materials(e.g., steel, cast iron, aluminum,), non-metallic materials (e.g.,concrete, grout, plastic, fiberglass), or combinations of materials(e.g., concrete filled fiberglass tube, plastic filled steel tube) thatexhibit a stiffness modulus greater than that of the matrix soil.

The presently disclosed soil reinforcement system that includes angledreinforcement elements provides certain advantages over conventionalprior art reinforcing methods, such as vertical reinforcing methods.Namely, the presently disclosed soil reinforcement system provides amore efficient mechanism for resisting shear forces than, for example,vertical reinforcing methods, by transferring applied shear forces inthe angled reinforcement element into axial compressive and tensileforces that act along the axis of the angled reinforcement element.

Generally, the presently disclosed soil reinforcement system employsangled reinforcement elements that are inserted into the ground toabsorb and/or resist seismic shear forces. Each of the angledreinforcement elements has a stiffness modulus that is greater than thestiffness modulus of the soil that it reinforces. During seismicshaking, each of the angled reinforcement elements acts in compressionor tension to resist the ground motions. This causes a reduction in theshear stress demand applied to the matrix soil, which, in turn, reducessoil liquefaction potential.

FIG. 1 and FIG. 2 illustrate a side view and top down view,respectively, of an example of a soil reinforcement system 100 thatincludes an arrangement of angled reinforcement elements 110 forabsorbing earthquake-induced seismic shear forces. The angledreinforcement elements 110 of soil reinforcement system 100 areinstalled across an area of matrix soil 150, which is the ground. Matrixsoil 150 can include, for example, any type or types of soil, any typeor types of rock, or any combinations of any type or types of soil androck and in any proportions.

The angled reinforcement elements 110 are formed, for example, ofmetallic materials (e.g., steel, cast iron, aluminum,), non-metallicmaterials (e.g., concrete, grout, plastic, fiberglass, wood), orcombinations of materials (e.g., concrete filled fiberglass tube,plastic filled steel tube) that exhibit a stiffness modulus greater thanthat of the matrix soil 150. The angled reinforcement elements 110 maybe inserted by drilling, driving, or other means. Examples of angledreinforcement elements 110 are shown and described with reference toFIG. 3 through FIG. 18.

The soil reinforcement system 100 can include any number and arrangementof angled reinforcement elements 110 as long as the goal of absorbingand/or resisting earthquake-induced seismic shear forces for reducingsoil liquefaction potential is substantially achieved. Namely, theangled reinforcement elements 110 can be arranged in any random ornon-random pattern that is useful for absorbing and/or resistingearthquake-induced seismic shear forces.

Wherein conventional prior art vertical (non-angled) elements, such asdriven pilings or drilled shafts, may be used to reduce seismic shearingstresses within the matrix soil, a limitation of the use of verticalelements is that if they are sufficiently slender, they resist asignificant portion of the applied shear stresses by bending, amechanism that results in less reduction of shear stresses within thereinforced matrix soil. This mechanism thus may significantly reduce theability of the vertical elements to reduce soil liquefaction potential.It is the intent of the presently disclosed soil reinforcement system100, which includes angled reinforcement elements 110, to overcome thislimitation.

In one example, the soil reinforcement system 100 includes an array orgrid of angled reinforcement elements 110 installed in matrix soil 150.The array or grid of angled reinforcement elements 110 can include anynumber of rows and columns, wherein each row and column can include anynumber of angled reinforcement elements 110. In the example shown inFIG. 1 and FIG. 2, soil reinforcement system 100 includes a 25×25 arrayof angled reinforcement elements 110 installed in matrix soil 150,wherein FIG. 1 shows one row (or line) of the 25×25 array of angledreinforcement elements 110. The presence of any arrangement of angledreinforcement elements 110 in the matrix soil 150 creates a reinforcedzone 115 in the matrix soil 150. Although not shown in FIG. 1, a secondarray of reinforcement elements that is orthogonal or transverse to thefirst array may also be installed to resist earthquake movement fromother directions.

One row of the angled reinforcement elements 110 is installed toreinforce a zone of width w1 generally from the proximal end of thefirst angled reinforcement element 110 to the proximal end of the lastangled reinforcement element 110, as shown in FIG. 1 and FIG. 2.Additionally, one column of the angled reinforcement elements 110 isinstalled to reinforce a zone of width w2 generally from the proximalend of the first angled reinforcement element 110 to the proximal end ofthe last angled reinforcement element 110, as shown in FIG. 2.

The rows of angled reinforcement elements 110 are installed at a spacings1. Spacing s1 can be constant or variable along the rows of angledreinforcement elements 110. The columns of angled reinforcement elements110 are installed at a spacing s2. Spacing s2 can be constant orvariable along the columns of angled reinforcement elements 110. Spacings1 and spacing s2 can be the same or different. In one example, both thespacing s1 and spacing s2 are a substantially constant spacing of about10 feet.

Additionally, each of the angled reinforcement elements 110 has a lengthL_(ARE) (see FIG. 3) and a diameter D_(ARE) (see FIG. 3). Further, theangled reinforcement elements 110 are installed at an angle θ withrespect to a surface 155 of the matrix soil 150 and to a depth dl intothe matrix soil 150. For a certain length L_(ARE), the depth dl of theangled reinforcement elements 110 and the lateral extent Lx of theangled reinforcing elements will depend on the angle θ.

The depth dl of the array of angled reinforcement elements 110 isselected based on the in-situ liquefaction susceptibility of the matrixsoil 150 and the consequences of liquefaction at a given depth profile.The depth dl of the angled reinforcement element 110 typically can befrom about 10 feet to about 70 feet, or is about 40 feet in one example.

The spacing s1 and spacing s2 and the diameter D_(ARE) of the angledreinforcement elements 110 are selected so that the transfer of theseismic shear stresses to the angled reinforcement elements 110 issufficient to reduce the stresses in the soil in order to mitigate orreduce the triggering of liquefaction. The spacing s1 and spacing s2 ofthe angled reinforcement element 110 typically can be from about 4 feetto about 30 feet, or is about 10 feet in one example. The diameterD_(ARE) of the angled reinforcement element 110 typically can be fromabout 2 inches to about 24 inches, or is about 12 inches in one example.The length L_(ARE) of the angled reinforcement element 110 typically canbe from about 15 feet to about 100 feet, or is about 57 feet in oneexample.

The angle θ of angled reinforcement elements 110 is selected based onboth installation and load transfer efficiency criteria. The angle θ ofthe angled reinforcement element 110 typically can be from about 45degrees to about 80 degrees, and is about 45 degrees in one example.

By way of example, FIG. 3 shows one angled reinforcement element 110. Inthis example, if the angle θ of the angled reinforcement element 110 isabout 45 degrees, in order to provide a depth dl of about 40 feet and alateral extent Lx (for a single angled reinforcement element 110) ofabout 40 feet, then the length L_(ARE) of the angled reinforcementelement 110 must be about 56.6 feet. If the 25×25 array of angledreinforcement elements 110 shown in FIG. 2 is installed in matrix soil150 according to FIG. 3 and if spacing s1 and spacing s2 are both about10 feet, then the width w1 of the reinforced zone 115 is about 240 feetand the width w2 of the reinforced zone 115 is about 240 feet.

FIG. 4 through FIG. 13 show and describe three examples of angledreinforcement elements 110 and respective methods of forming the threeexamples of angled reinforcement elements 110. However, the presentlydisclosed angled reinforcement elements 110 are not limited to thesethree examples only.

In one embodiment and referring now to FIG. 4 and FIG. 5, the angledreinforcement element 110 may consist of concrete-filled or grout-filledshafts that are formed in the ground. For example, FIG. 4 shows amandrel 410 that is driven or pushed into the matrix soil 150 to form anelongated hold or cavity (or shaft). The mandrel 410 is typically hollow(but typically with a removable closed end driving cap, for example,which can be valved or sacrificial) and forms a hollow channel or shaftin the matrix soil 150. Then, the mandrel 410 is filled with a flowablematerial 415. The flowable material 415 can be, for example, concrete orgrout. Once the mandrel 410 is filled (or during filling), but beforethe flowable material 415 is cured to a hardened state, the mandrel 410is extracted from the matrix soil 150, leaving behind an angled channelor column of, for example, concrete or grout in the matrix soil 150, asshown in FIG. 5. Namely, FIG. 5 shows the resulting angled reinforcementelement 110 (minus the mandrel 410), which is formed of the curedflowable material 415. In another example, instead of using the hollowmandrel 410, an angled hole or cavity (or shaft) can be drilled in thematrix soil 150 using a hollow-flight or solid-flight auger and theangled hole is then filled with the flowable material 415. Optionallyand referring now to FIG. 6, before the flowable material 415 is cured,steel reinforcing rods 420 may be installed in the flowable material415. The presence of steel reinforcing rods 420 allows the resultingangled reinforcement element 110 to better resist both compressive andtensile loads.

FIG. 7 shows a flow diagram of an example of a method 700 of forming andinstalling the angled reinforcement element 110 that is shown anddescribed with reference to FIG. 4, FIG. 5, and FIG. 6. Whereas method700 describes a method of forming one angled reinforcement element 110,the soil reinforcement system 100 is formed by repeating method 700 foreach of the multiple angled reinforcement elements 110 in the soilreinforcement system 100. Method 700 may include, but is not limited to,the following steps.

At a step 710, the flowable material from which the angled reinforcementelement 110 is to be formed is selected and prepared. In one example andreferring now to FIG. 4, the flowable material 415 can be, for example,concrete or grout. If concrete is selected, then the concrete isprepared. If grout is selected, then the grout is prepared.

At a step 715, at any desired angle θ, an elongated shaft is formed inthe ground according to the desired element length L_(ARE) and elementdiameter D_(ARE). In one example and referring again to FIG. 4, themandrel 410 is driven into the matrix soil 150 to form the elongatedshaft. The size of the mandrel 410 depends on the desired element lengthL_(ARE) and the desired element diameter D_(ARE). In one example, themandrel 410 is about 50 feet long, has a diameter of about 1 foot, andis driven into the matrix soil 150 at about a 45-degree angle. Inanother example, such as in cohesive soils, instead of using the mandrel410, a hole is drilled in the matrix soil 150. In one example, the holeis about 50 feet long, has a diameter of about 1 foot, and is drilledinto the matrix soil 150 at about a 45-degree angle.

At a step 720, the elongated shaft is filled with the flowable materialselected in step 710. In one example, the mandrel 410 is filled with theflowable material 415, such as concrete or grout, and then the mandrel410 is extracted from the matrix soil 150 (or the mandrel is extractedwhile the flowable material is filled), leaving behind a channel orcolumn of concrete or grout in the matrix soil 150, as shown in FIG. 5.In another example (e.g., drilling), the hole is filled with theflowable material 415, such as concrete or grout, to form the angledchannel or column of concrete or grout in the matrix soil 150.

At an optional step 725, reinforcing rods are installed in the elongatedshaft. For example, before the flowable material 415 is cured, steelreinforcing rods 420 may be installed in the flowable material 415, asshown in FIG. 6.

In yet another embodiment and referring now to FIG. 8 and FIG. 9, theangled reinforcement element 110 may consist of a hollow tube 810comprised of, for example, concrete, steel, aluminum, plastic,fiberglass, composite materials, or any combinations thereof.Optionally, the hollow tube exhibits properties that allow it to resistapplied tensile loads. The hollow tube typically has a closed end(pointed or otherwise) on one end for driving. The hollow tube 810 isdriven into the matrix soil 150 and then filled with a flowable material815. Examples of flowable material 815 include, but are not limited to,concrete; grout; granular materials, such as gravel, aggregate, sand,recycled concrete, crushed glass, or other flowable materials; and anycombinations thereof. Granular infill materials may be compacted inplace using a compaction device (not shown) to increase their densityand the composite stiffness of the angled reinforcement element 110.Optionally, steel reinforcing rods, such as the steel reinforcing rods420 shown in FIG. 6, may be installed in the flowable material 815.Additionally, flowable material 815 can include materials with highpermeabilities that facilitate the drainage of excess pore waterpressures during and after seismic events.

FIG. 10 shows a flow diagram of an example of a method 1000 of formingand installing the angled reinforcement element 110 that is shown anddescribed with reference to FIG. 8 and FIG. 9. Whereas method 1000describes a method of forming one angled reinforcement element 110, thesoil reinforcement system 100 is formed by repeating method 1000 foreach of the multiple angled reinforcement elements 110 in the soilreinforcement system 100. Method 1000 may include, but is not limitedto, the following steps.

At a step 1010, the flowable material from which the angledreinforcement element 110 is to be formed is selected and prepared.Referring now to FIG. 8, the flowable material 815 can be, for example,concrete; grout; granular materials, such as gravel, aggregate, sand,recycled concrete, crushed glass, or other flowable materials; and anycombinations thereof. If concrete or grout is selected, then theconcrete or grout is prepared. If granular materials are selected, thenthe granular materials are prepared.

At a step 1015, an elongated shaft is formed in ground to any desireddepth dl and diameter D_(ARE) and at any desired angle θ. In oneexample, a hole is drilled in the matrix soil 150. For example, a 1-footdiameter hole is drilled in the matrix soil 150 at about a 45-degreeangle and to a depth dl of about 40 feet. It is understood that thisstep may be optional if the hollow tube 810 can be driven in to thematrix soil 150 without the pilot shaft being needed.

At a step 1020, a hollow casing or tube is driven or pushed into theshaft in the matrix soil 150. For example and referring to FIG. 8 andFIG. 9, hollow tube 810 is driven or pushed into the shaft in the matrixsoil 150. The hollow tube 810 can be formed, for example, of concrete,steel, aluminum, plastic, fiberglass, composite materials, or anycombinations thereof.

At a step 1025, the elongated hollow casing or tube is filled with theflowable material selected in step 1010. In one example, the hollow tube810 is filled with the flowable material 815, such as concrete; grout;granular materials, such as gravel, aggregate, sand, recycled concrete,crushed glass, or other flowable materials; and any combinationsthereof, as shown in FIG. 8 and FIG. 9.

At an optional step 1030, reinforcing rods are installed in the hollowcasing or tube. For example, before the flowable material 815 is cured,steel reinforcing rods 420 (see FIG. 6) may be installed in the flowablematerial 815.

While FIG. 4 through FIG. 10 describe examples of angled reinforcementelements 110 that are formed directly within the matrix soil 150, FIG.11, FIG. 12, and FIG. 13 describe an example of an angled reinforcementelement 110 that is formed separately outside of the matrix soil 150 andthen installed into the matrix soil 150.

In another embodiment and referring now to FIG. 11 and FIG. 12, theangled reinforcement element 110 may consist of an elongated solid andrigid element that can be driven or pushed into the matrix soil 150using, for example, piling equipment (not shown). In particular, thematerial that is used to form the solid and rigid angled reinforcementelement 110 has a material stiffness value greater than that of thematrix soil 150. Examples of such materials include, but are not limitedto, steel, concrete, fiberglass, wood piling, plastic, compositematerials, and any combinations thereof. The reinforcement element 110embodiment as shown in FIG. 12 is circular in cross-section (such as apointed cylinder), but it is understood that a variety of cross-sectionsmay be used such as, for example, square, rectangle, T-shaped, X-shaped,or cross-shaped.

FIG. 13 shows a flow diagram of an example of a method 1300 of formingand installing the angled reinforcement element 110 that is shown anddescribed with reference to FIG. 11 and FIG. 12. Whereas method 1300describes a method of forming one angled reinforcement element 110, thesoil reinforcement system 100 is formed by repeating method 1300 foreach of the multiple angled reinforcement elements 110 in the soilreinforcement system 100. Method 1300 may include, but is not limitedto, the following steps.

At a step 1310, an elongated, solid, rigid element is formed accordingto the desired length L_(ARE) and diameter D_(ARE) of the angledreinforcement element 110. For example, the elongated, solid, rigidelement can be formed of steel, concrete, fiberglass, wood piling,plastic, composite materials, and any combinations thereof to create anangled reinforcement element 110. In one example, the resultingelongated, solid, rigid angled reinforcement element 110 is about 50feet long and has a diameter of about 1 foot.

At a step 1315, at any desired angle θ, the elongated, solid, rigidelement is driven or pushed into the matrix soil 150. For example, theresulting elongated, solid, rigid angled reinforcement element 110 isdriven or pushed into the matrix soil 150 using piling equipment (notshown).

During seismic events, shear stresses are transmitted from bedrockupwards through the soil profile. When seismic shear stresses areapplied to saturated loose deposits of sand, silt, and low plasticityclay, the soil particles have a tendency to contract (move towards eachother) and the water that exists in the pore spaces becomes pressurized.As the pore water pressure increases, the effective stress in the soildecreases resulting in reduction of soil shear strength. With time, theelevated pore water pressure causes the pore water to vent, whichresults in seismically-induced settlement. It is the intent of thepresently disclosed soil reinforcement system 100 to reduce themagnitude of the peak shear forces applied to the soil at a givenelevation within the reinforced zone 115 (see FIG. 1 and FIG. 2) bytransferring these shear forces to the angled reinforcement elements110.

Shear forces applied to heterogeneous materials de-aggregate intocomponent shear forces where the magnitudes of the component shearforces depend on the relative stiffnesses and areas of the heterogeneouscomponents. Referring to FIG. 14, the shear forces V_(EQ) that propagateupward through the soil profile during seismic events may be resisted inpart by the shear force V_(S) applied to the matrix soil 150 between theangled reinforcement elements 110 and the shear force V_(P) applied tothe angled reinforcement elements 110. The sum of shear force V_(S) andshear force V_(P) must equal shear forces V_(EQ) to satisfy equilibrium.The magnitudes of shear force V_(S) and shear force V_(P) depend on thecomponent area encompassed by shear force Vs and the component areaencompassed by shear force Vp and also depends on the relative stiffnessof the components. The higher the percentage of area covered by theangled reinforcement element 110 and the higher the stiffness of theangled reinforcement element 110, the greater the magnitude of shearforce V_(P) relative to shear force V_(S). It is the intent of thepresent invention to decrease the magnitude of shear force V_(S) to alevel that is insufficient to cause the matrix soil to liquefy.

The shear force V_(P) that is applied to the angled reinforcementelement 110 is in turn resisted by the development of axial compressiveor tensile stresses within the element and by transverse shear forceswithin the element. Referring to FIG. 15, the shear force V_(P) that isapplied to the angled reinforcement element 110 is made up of vectorcomponents transverse to, and along the axis of element 110. Usinggeometry, the magnitude of axial force P_(P) is computed as the productof applied shear force V_(P) and the sine of the angle α, which is theangle of inclination. Thus, the smaller the angle α, the greater thevalue of axial force P_(P) required to achieve equilibrium with theapplied load of shear force V_(P). The axial force P_(P) is, in turn,resisted by the sum of the unit tractile forces F_(S) that develop alongthe element shaft. Examples of tractile forces F_(S) are tractilecohesion and friction resistance. Thus, applied shear force V_(P)results in axial force P_(P), which is resisted by the sum of thetractile forces F_(S) acting along its shaft. It is the intent of thepresent invention to distribute applied shear loads along the shaft ofthe angled reinforcement element 110.

The description above is applicable for a single shear force to beapplied to the angled reinforcement element 110. However, earthquakescause shear stress to propagate throughout the soil profile resulting ina spectrum of shear stress applied at various elevations at varioustimes. Referring to FIG. 16, a plot 1600 is shown of the sinusoidalshear stress distributions that may occur within the ground at twodifferent discrete times (e.g., time A and time B) during a simulatedearthquake. In accordance with the simulated input motion, the shearstress distribution has a sinusoidal shape. At time A, peak shearstresses occur at depths with peak values occurring at depths indicatedby depths 1, 2, and 3. At depths 1 and 3, the peak shear stresses Veq1and Veq3 are applied in the left direction. At depth 2, the peak shearstress Veq2 is applied in the right direction. At depths midway betweendepths 1 and 2 and midway between depths 2 and 3, the shear stress iszero. At time B, the shear wave has moved up in the soil profile suchthat no shear stresses are experienced at depths 1, 2, and 3. Rather,peak shear stresses are experienced at the midway depths between depths1 and 2 and between depths 2 and 3. FIG. 16 shows that the seismicstresses applied to the reinforced depth H of a given soil profilechange with time and may consist of multiple stresses resulting ineither compression or tension within the angled reinforcement element110.

A schematic representation of the application of two shear forces, eachacting in opposite directions, is shown in FIG. 17. Namely, FIG. 17illustrates the case of a rightward-acting shear force V_(P1) applied tothe upper portion of the angled reinforcement element 110 and aleftward-acting shear force V_(P2) applied to the lower portion of theangled reinforcement element 110. Shear force is the product of shearstress applied over a tributary area. In this case, the downwardlyangled compressive force P_(P1) is resisted by the upwardly angledcompressive force P_(P2) and the tractile forces represented by the sumof tractile forces F_(S1) that acts to resist P_(P1) are negated by thetractile forces represented by the sum of tractile forces F_(S2) actingto resist the upwardly angled compressive force P_(P2). The net resultof the load transfer mechanisms depicted in FIG. 17 are that the angledreinforcement element 110 internally resists the applied shear forcesthat act simultaneously but in two different directions on the soilprofile. It is the intent of the presently disclosed soil reinforcementsystem 100 to capture these applied counteracting loads to reduce thepotential for matrix soil liquefaction.

There are unlimited combinations of forces applied to the angledreinforcement element 110 with respect to time during an applied seismicevent. Mathematical solutions can be achieved for many combinations,however, using computer numerical simulations. It is the intent of thepresently disclosed soil reinforcement system 100 to capture many ofthese counteracting modes of applied forces.

The angled reinforcement elements 110 must exhibit a stiffness modulusgreater than the matrix soil that they are reinforcing. Elements with ahigh interface friction coefficient exhibit improved functionalitycompared to those with low interface friction coefficients because oftheir ability to transmit applied shear forces V_(P) into the angledreinforcement elements 110 and then in turn transmit these loads out ofthe angled reinforcement elements 110 through the sum of tractile forcesF_(S) transferred from the angled reinforcement elements 110 to thesoil.

Referring again to FIG. 1 and FIG. 2, which shows the angledreinforcement elements 110 arranged in an array or grid pattern, if theangled reinforcement elements 110 are designed to resist compressiveforces only, then a second array or grid of angled reinforcementelements 110 that are angled 180 degrees in plan view from the firstarray or grid is required. Further, to resist seismic forces that mayoccur orthogonal to the reinforced zone 115 shown in FIG. 1 and FIG. 2,an array or grid of angled reinforcement elements 110 is required in thetransverse direction to that shown in FIG. 1 and FIG. 2, wherein thetransverse direction may be perpendicular or not perpendicular to thefirst array or grid pattern.

Example

A numerical analysis was performed to simulate the effects of appliedearthquakes to the array or grid of angled reinforcement elements 110shown in FIG. 1 and FIG. 2. The numerical analysis consisted of atwo-dimensional plane strain model created using the software SAP 2000.The model included the following features: (a) the matrix soil 150 andangled reinforcement element 110 respond linearly; (b) perfect straincompatibility is developed at the junction in between the angledreinforcement elements 110 and the grid nodes; (c) vertical, horizontal,and rotational degrees of freedom of nodes along the left and rightlateral boundaries of the finite element mesh shown in FIG. 1 displaceequally; and (d) the Corralitos station acceleration time historyrecorded during the Loma Prieta earthquake, which has a peak groundacceleration of 0.48 g.

The angled reinforcement elements 110 were modeled as one-foot diameterframe elements as available in the SAP program. The frame elementsdevelop moments, shear, and axial forces when loaded. The modulus ofelasticity for the piles was varied during the investigation. Energydissipation for the elastic model is handled in SAP 2000 throughRayleigh damping. An iterative procedure was used to introduce a dampingratio of 5% for the first and second modes of vibration. The modelincluded a built-in algorithm which extrapolates damping for highermodes. A check of the damping coefficients was made by comparing: a) thefundamental period of vibration (T) obtained from SAP 2000 to b) thatcalculated using closed form equations.

The results of the numerical studies for the angled reinforcementelements 110 are shown in FIG. 18. Namely, FIG. 18 shows a plot 1800 ofthe normalized shear stress vs. normalized depth for angledreinforcement elements 110 on a grid spacing of 10 ft×10 ft. The resultsare shown in terms of the normalized shear stresses computed at pointsalong a vertical section through the center of the finite element meshshown in FIG. 1 for a given soil elastic modulus value, E_(soil), wherethe normalized shear stress is defined as the maximum shear stress inthe matrix soil computed by analyses containing inclined elementsnormalized by the maximum shear stress in the matrix soil computed byanalyses that do not contain inclined elements.

Lower values of normalized shear stress indicate greater effectivenessof the angled reinforcement elements 110 in resisting applied shearstresses and forces. FIG. 18 shows plots of the normalized shear stressvs. normalized depth for angled reinforcement elements 110 for a gridspacing of angled reinforcement elements 110 that are 10 feet on-centerfor ground spacing. Normalized depth is the ratio of the depth from theground surface in the model to the depth of the reinforced zone 115shown in FIG. 1 and FIG. 2. FIG. 18 shows that normalized shear stressescomputed using the model range from 0.37 to 0.95 within the upper 90percent of the reinforced soil profile. Lower values of normalized shearare achieved for higher E_(pile)/E_(soil) ratios. This means that thestiffer the angled reinforcement element 110 is relative to the soil,the more effective it is in reducing the shear stresses and forcesapplied to the matrix soil 150.

By contrast, FIG. 19 shows the results an equivalent set of numericalanalyses applied to an array of conventional prior art vertical(non-angled) elements (not shown); namely, elements installed at angleθ=about 90 degrees. The vertical elements are also spaced in an array 10feet on-center for ground spacing. Namely, FIG. 19 shows a plot 1900 ofthe normalized shear stress vs. normalized depth for vertical elementson a grid spacing of 10 ft×10 ft. FIG. 19 shows that the verticalelements achieve normalized stress ratios ranging from approximately 0.8to 1.0 over the upper 90 percent of the soil profile. The highernormalized stress ratios relative to those shown in FIG. 18 indicateless effectiveness at resisting applied shear stresses.

Comparing the results shown in plot 1800 of FIG. 18 to those shown inplot 1900 of FIG. 19 for an E_(pile) to E_(soil) ratio of 400 at anormalized depth of 0.5, a normalized stress ratio of 0.52 is achievedfor the angled reinforcement elements 110 and a normalized stress ratioof 0.87 is achieved for the conventional vertical elements. This meansthat the angled reinforcement elements 110 reduce about 70% more shearforce than resisted by the conventional prior art vertical elements atthe same stiffness and same spacing. These results demonstrate theefficiency of the presently disclosed soil reinforcement system 100 thatincludes the angled reinforcement elements 110.

Following long-standing patent law convention, the terms “a,” “an,” and“the” refer to “one or more” when used in this application, includingthe claims. Thus, for example, reference to “a subject” includes aplurality of subjects, unless the context clearly is to the contrary(e.g., a plurality of subjects), and so forth.

Throughout this specification and the claims, the terms “comprise,”“comprises,” and “comprising” are used in a non-exclusive sense, exceptwhere the context requires otherwise. Likewise, the term “include” andits grammatical variants are intended to be non-limiting, such thatrecitation of items in a list is not to the exclusion of other likeitems that can be substituted or added to the listed items.

For the purposes of this specification and appended claims, unlessotherwise indicated, all numbers expressing amounts, sizes, dimensions,proportions, shapes, formulations, parameters, percentages, parameters,quantities, characteristics, and other numerical values used in thespecification and claims, are to be understood as being modified in allinstances by the term “about” even though the term “about” may notexpressly appear with the value, amount or range. Accordingly, unlessindicated to the contrary, the numerical parameters set forth in thefollowing specification and attached claims are not and need not beexact, but may be approximate and/or larger or smaller as desired,reflecting tolerances, conversion factors, rounding off, measurementerror and the like, and other factors known to those of skill in the artdepending on the desired properties sought to be obtained by thepresently disclosed subject matter. For example, the term “about,” whenreferring to a value can be meant to encompass variations of, in someembodiments, ±100% in some embodiments ±50%, in some embodiments ±20%,in some embodiments ±10%, in some embodiments ±5%, in some embodiments±1%, in some embodiments ±0.5%, and in some embodiments ±0.1% from thespecified amount, as such variations are appropriate to perform thedisclosed methods or employ the disclosed compositions.

Further, the term “about” when used in connection with one or morenumbers or numerical ranges, should be understood to refer to all suchnumbers, including all numbers in a range and modifies that range byextending the boundaries above and below the numerical values set forth.The recitation of numerical ranges by endpoints includes all numbers,e.g., whole integers, including fractions thereof, subsumed within thatrange (for example, the recitation of 1 to 5 includes 1, 2, 3, 4, and 5,as well as fractions thereof, e.g., 1.5, 2.25, 3.75, 4.1, and the like)and any range within that range.

Although the foregoing subject matter has been described in some detailby way of illustration and example for purposes of clarity ofunderstanding, it will be understood by those skilled in the art thatcertain changes and modifications can be practiced within the scope ofthe appended claims.

That which is claimed:
 1. A method of installing an array of angled soilreinforcement elements to absorb seismic shear stresses in a soilmatrix, comprising inserting an array of angled soil reinforcementelements into a soil matrix at a determined angle and to a determineddepth, wherein each of the soil reinforcement elements of the array ofangled soil reinforcement elements comprises a material that exhibits astiffness modulus greater than the stiffness modulus of the soil matrixand wherein seismic shear stresses imparted from seismic activity areabsorbed by the array of angled soil reinforcement elements, thusreducing a potential for soil liquefaction, wherein the soilreinforcement elements are spaced from each other such that none of theangled soil reinforcement elements within the array are in directcontact with another angled soil reinforcement element within the array.2. The method of claim 1, wherein the soil reinforcement elements areinserted in the soil matrix by drilling means.
 3. The method of claim 1,wherein the angled soil reinforcement elements are inserted in the soilmatrix by driving means.
 4. The method of claim 1, wherein the angledsoil reinforcement elements within the array comprise metallic material.5. The method of claim 1, wherein the angled soil reinforcement elementswithin the array comprise non-metallic material.
 6. The method of claim1, wherein the angled soil reinforcement elements within the arraycomprise a combination of metallic and non-metallic materials.
 7. Themethod of claim 1, wherein the determined depth is selected based on thein-situ liquefaction susceptibility of the matrix soil.
 8. The method ofclaim 1, wherein the spacing and diameter of the array of angled soilreinforcement elements is determined such that the transfer of theseismic shear stresses to the array of angled soil reinforcementelements is sufficient to reduce shear strains in the soil to reduce thetriggering of liquefaction.
 9. The method of claim 1, wherein the angleof inclination is a predetermined angle based on desired installationand load transfer efficiency criteria.
 10. The method of claim 1,wherein the angled soil reinforcement elements comprise cast-in-placeshafts that are formed in the soil matrix.
 11. The method of claim 10,wherein the shafts are filled with one or more of concrete and grout.12. The method of claim 11, wherein the angled soil reinforcementelements are installed using a mandrel driven or pushed into the groundand filled with the one or more of concrete and grout, and then themandrel is extracted.
 13. The method of claim 11, wherein the methodfurther comprises forming an angled drilled hole in the soil matrix andfilling the angled hole with the one or more of concrete and grout. 14.The method of claim 11, wherein reinforcing steel is added to the one ormore of concrete and grout shafts prior to curing.
 15. The method ofclaim 1, wherein the angled soil reinforcement elements are installed inthe soil matrix by piling equipment and are driven or pushed into thesoil matrix and are filled with an in-fill after driving.
 16. The methodof claim 1, wherein the angled soil reinforcement elements are hollowand are filled with an in-fill material after installation.
 17. Themethod of claim 16, wherein the in-fill material comprises one or moreof concrete, grout, gravel, aggregate, sand, recycled concrete, crushedglass, and other flowable or pumpable material.
 18. The method of claim16, wherein the in-fill material is compacted in place using acompaction device.
 19. The method of claim 1, wherein the angled soilreinforcement elements comprise a permeable material that facilitatesdrainage of excess pore water pressures during and after seismic events.20. The method of claim 1, wherein the array of angled soilreinforcement elements are installed on a grid pattern.
 21. The methodof claim 20, further comprising a second grid pattern of two or moreangled soil reinforcement elements angled 180 degrees from the firstgrid pattern of the array of angled soil reinforcement elements.
 22. Themethod of claim 20, further comprising a second grid pattern of two ormore angled soil reinforcement elements installed in a transversedirection relative to a direction of the first grid pattern of the arrayof angled soil reinforcement elements.
 23. The method of claim 22,wherein the transverse direction is perpendicular to the first gridpattern.
 24. The method of claim 22, wherein the transverse direction isnot perpendicular to the first grid pattern.
 25. An array of angled soilreinforcement elements for absorbing seismic shear stresses in a soilmatrix, the array of angled soil reinforcement elements installed in asoil matrix each at a determined angle relative to the soil matrix andto a determined depth in the soil matrix, the array of soilreinforcement elements each comprising a material that exhibits astiffness modulus greater than the stiffness modulus of the soil matrixwherein seismic shear stresses are absorbed by the array of angled soilreinforcement elements to reduce potential for soil liquefaction,wherein each of the angled soil reinforcement elements are spaced fromeach other such that none of the angled soil reinforcement elements arein direct contact with another angled soil reinforcement element withinthe array, and wherein spacing between each angled soil reinforcementelement of the array is about four feet to about thirty feet.
 26. Asystem for installing an array of angled soil reinforcement elements toabsorb seismic shear stresses, comprising: a) an array of angled soilreinforcement elements; and b) a device for installing the array ofangled soil reinforcement elements into a soil matrix at a determinedangle and to a determined depth; wherein each angled soil reinforcementelement of the array of angled soil reinforcement elements comprise amaterial that exhibits a stiffness modulus greater than the stiffnessmodulus of the soil matrix wherein seismic shear stresses in the soilmatrix imparted from seismic activity are absorbed by the array ofangled soil reinforcement element to reduce potential for soilliquefaction, wherein each of the angled soil reinforcement elements arespaced from each other such that none of the angled soil reinforcementelements are in direct contact with another angled soil reinforcementelement within the array, and wherein spacing between each angled soilreinforcement element of the array is about four feet to about thirtyfeet.
 27. The system of claim 26 wherein the device for installing thearray of angled soil reinforcement elements into the soil matrixcomprises a piling device for driving or pushing each of the angled soilreinforcement elements into the soil matrix.
 28. The system of claim 26wherein the device for installing the array of angled soil reinforcementelements into the soil matrix comprises a mandrel driven or pushed intothe soil matrix, wherein the mandrel is filled with one or more of groutand concrete, and then the mandrel is extracted.
 29. The system of claim26 wherein the device for installing the array of angled soilreinforcement elements into the soil matrix comprises a drilling devicewherein the drilling device forms an angled drilled hole in the soilmatrix and the hole is then filled with one or more of concrete andgrout.